First, who is your victim? I’d include name, physical description, and social status at least.
How did your victim die? Sword through the heart? Decapitated? Drowned? Poisoned?
Where did your victim die? In a dungeon? In a study? In someone’s bedroom? In the garden? In a hotel room? In the wilderness?
When did your victim die? First thing in the morning? Day? Dusk? Dead of night?
Who could have killed the victim? These are your suspects. It’s not as important to flesh out the specifics of why and how they’re suspects right now; at this point, you’re just building a list of people with some personal relationship or physical proximity to the victim. Think relatives, friends, enemies, and caretakers. I’ve always had at least 3 suspects, to give the PCs plenty of potential leads.
Now you can build a table. On one side of a piece of paper (or a spreadsheet), write each suspect’s name in a column. Along the top of the paper, write the following column headers: Means, Motive, and Opportunity.
And now you get to completely make stuff up!
Every suspect who had access to the murder weapon gets a note in the “Means” column, explaining how they have access to it.
Every suspect who had a reason to kill the victim gets a note explaining that reason in the “Motive” column.
The “Opportunity” column is a little special. You can note both those suspects who were free and could have been with the victim at the time of the crime, and those suspects who absolutely were not free and couldn’t possibly have been with the victim at the time of the crime. You can also note any significant details about the circumstances; if the suspect was with several other people at the time of the murder, who were they?
Importantly, you don’t have to fill in every space! Some suspects won’t have a motive. Some won’t have access to the murder weapon.
Once you’re satisfied, look back at your table as a whole. Any suspect with all of the columns filled out, and where the Opportunity column indicates they were free at the time of the murder, is the murderer. If you have multiple murderers–that is, more than one suspect has all three columns filled out–that’s great! They’re all potential murderers. You don’t have to decide.
This is all I’ve ever needed to run a murder mystery. In the game, I explain the situation, introduce the suspects, and let the players investigate. Once they’ve narrowed their list of suspects down to one of the potential murderers (someone with the Means, Motive, and Opportunity), I make that the actual murderer and give the PCs the satisfaction of being right.
Hope this helps!